Subdividing face doesn't automatically subdivide adjacent face
So...It is, but it isn't.

I'm betting you are watching some older tutorial videos (circa 2013) because that was old Blender subdivide behavior (circa v2.53).  Subdividing or otherwise changing the edge-count of a polygon ran the risk of an edge explosion to keep all polygons on a mesh either quads(4 edges) or triangles (3 edges).  

Blender, as of around version 2.56, recieved N-Gon support.  N-Gons is the colloquialism that refers to polygons with 5+ edges, and Blender then began to hold them more or less as-is.  This allows for more or less non-destructive polygon slicing, which is what you are experiencing.

Under the hood, it is tracking just a bunch of triangles though.  If you want to see and manipulate those triangles, triangulate is ctrlt while the faces in question are selected.   

You might want to find more recent tutorials, as well.